Question: Solve for $x$ and $y$ using substitution. ${-2x+3y = -5}$ ${x = 3y+7}$
Solution: Since $x$ has already been solved for, substitute $3y+7$ for $x$ in the first equation. ${-2}{(3y+7)}{+ 3y = -5}$ Simplify and solve for $y$ $-6y-14 + 3y = -5$ $-3y-14 = -5$ $-3y-14{+14} = -5{+14}$ $-3y = 9$ $\dfrac{-3y}{{-3}} = \dfrac{9}{{-3}}$ ${y = -3}$ Now that you know ${y = -3}$ , plug it back into $\thinspace {x = 3y+7}\thinspace$ to find $x$ ${x = 3}{(-3)}{ + 7}$ $x = -9 + 7$ ${x = -2}$ You can also plug ${y = -3}$ into $\thinspace {-2x+3y = -5}\thinspace$ and get the same answer for $x$ : ${-2x + 3}{(-3)}{= -5}$ ${x = -2}$